0

I'm trying to prove that (P → Q) ↔ (¬Q → ¬P) using Fitch.

I know I have to prove two subproofs.

1) P → Q 2)¬Q → ¬P

closed as off-topic by Joseph Weissman Jan 19 '16 at 0:17

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "While this question may be related to philosophy or occur in a philosophical context, the question itself doesn't seem to be about philosophy, and is therefore not a good fit for our site." – Joseph Weissman
If this question can be reworded to fit the rules in the help center, please edit the question.

2

Hint

For the first part :

1) P → Q --- premise

2) ¬Q --- assumed [a]

3) P --- assumed [b]

4) Q --- from 1) and 3) by →-elimination

5) from 2) and 4)

6) ¬P --- from 3) and 5) by ¬-introduction, discharging [b]

7) ¬Q → ¬P --- from 2) and 6) by →-introduction, discharging [a].

The other part of the proof is similar.

Not the answer you're looking for? Browse other questions tagged or ask your own question.